Am I still able to target attacking creatures with Spires of Orazca's ability if they are not tapped (if they have Vigilance for example)?
Yes, you can.
Whenever you have to select a target for a spell or ability, the target has to be legal when you select it and when that spell or ability resolves. "Target attacking creature" means that the targeted object has to be a creature permanent, and it must be currently attacking. No other properties matter. To untap the targeted creature and to remove it from combat are effects of that ability. If you target an attacking creature that is untapped, for example because it has vigilance, then the Spire's ability does as much as possible when it resolves. You can't untap the targeted creature because it's already untapped, but you can remove it from combat, and that's what happens.
Yes, since the description of the target is only "target attacking creature an opponent controls", with no mention of it being tapped.
Then when the ability resolves it simply does not untap the creature if it is not tapped, as specified in the rules for effects:
609.3. If an effect attempts to do something impossible, it does only as much as possible.
Yes. The conditions for targeting with Spires of Orazca are "target attacking creature an opponent controls" if you could not use spires on a vigilant creature the condition would have to be "target tapped and attacking creature an opponent controls". Because of the way it was worded, any attacking opponent creature meets the requirement, regardless of it's tapped or untapped status.
In general the only time tapped or untapped status of a card matters for abilities is when changing that status is part of the cost, not the effect. You couldn't attempt to use Gilder Bairn's untap ability while he is already untapped because it is part of the cost, and that cost needs to be paid in full, but if it had been part of the effect, that portion of the effect would just not happen and the rest would, as seen in the comprehensive rules:
609.3 If an effect attempts to do something impossible, it does only as much as possible.
The reason Maze of Ith type effects untap is to effectively undo the declaration as an attacker, or as much of it as possible since any effects that go along with declaring the attacker [such as battlecry or legion] would still hit stack, and leave the opponent in the same position as they would have been had they not attacked with that creature, now it is able to tap for abilities or be used as a blocker against your attacks.